Why don't people use projected Bellman error with deep neural networks?
I have found some clues in Maei's thesis (2011): “Gradient Temporal-Difference Learning Algorithms.”

According to the thesis: 


GTD2 is a method that minimizes the projected Bellman error (MSPBE).
GTD2 is convergent in non-linear function approximation case (and off-policy).
GTD2 converges to a TD-fixed point (same point as semi-gradient TD).
GTD2 is slower to converge than usual semi-gradient TD. 



  It doesn't readily apply to non-linear function approximation.


No, it does.


  It doesn't yield a good solution. 


No, it does. TD-fixed point is the same point for the solution of semi-gradient TD (which is generally used). There is no edge on that.

The only explanation seems to be practical convergence rate.

To quote his words: 


  Some of our empirical results suggest that gradient-TD method maybe slower than conventional TD methods on problems on which conventional TD methods are sound (that is, on-policy learning problems).